ok, in that case, put the LJ VIN on the dash, that'll keep the emissions people happy. I don't know if you'd mentioned the years but if so I missed it so I've been assuming based on statistical likelihood/production numbers since most LJ's are 05-06.
Again, note that you ONLY need a Jeep PCM if you absolutely insist on keeping the factory cluster. If you do choose to keep the factory cluster, you just need the PCM that matches the cluster. Use the TJ PCM with the TJ cluster or the LJ PCM with the LJ cluster. IMO, keeping both LJ will probably save you a fair bit of work because I have to assume the harnesses would differ significantly.
The LS PCM will be what the scanner sees and connects to, so the VIN doesn't matter, but if for some reason you end up swapping the PCM, cluster, and the connecting harness from the TJ, the TJ PCM should be able to be programmed for a new VIN. But again...no one is ever gonna hook up to it so it matters none whatsoever.